Statistics for Environmental Engineers

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FeCl3 (g/L)




H2SO4 (g/L)




Oil (mg/L)




This test seems to confirm that the best combination is 1.3 g/L of FeCl3 and 0.1 g/L of H2SO4.

Unfortunately, this experiment, involving eight runs, leads to a wrong conclusion. The response of oil removal efficiency as a function of acid and iron dose is a valley, as shown in Figure 22.3. The first one-at-a-time experiment cut across the valley in one direction, and the second cut it in the perpendicular direction. What appeared to be an optimum condition is false. A valley (or a ridge) describes the response surface of many real processes. The consequence is that one-factor-at-a-time experiments may find a false optimum. Another weakness is that they fail to discover that a region of higher removal efficiency lies in the direction of higher acid dose and lower ferric chloride dose.

We need an experimental strategy that (1) will not terminate at a false optimum, and (2) will point the way toward regions of improved efficiency. Factorial experimental designs have these advantages. They are simple and tremendously productive and every engineer who does experiments of any kind should learn their basic properties.

We will illustrate two-level, two-factor designs using data from the emulsion breaking example. A two-factor design has two independent variables. If each variable is investigated at two levels (high and

One-factor-at-a-time experimental design gives a false optimum

Desired region of operation

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